At 40∘C, a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod when it is heated to 240∘C? The coefficients of linear expansion of brass and steel are 2.0×10−5 ∘C−1 and 1.2×10−5 ∘C−1 respectively.
0.32 cm
The increase in the length of the brass rod, Δlb=2×10−5×0.5×(240−40)=0.2 cm
The increase in the length of the steel rod, Δls=1.2×10−5×0.5×(240−40)=0.12 cm
∴ Increase in the length of the composite rod, Δl=Δlb+Δls=0.20+0.12=0.32 cm
Hence, the correct choice is (c).